INVESTIGATION OF EQUIVALENT POROUS MEDIUM PERMEABILITY IN NETWORKS OF DISCONTINUOUS FRACTURES

The purpose of this study is to determine when a fracture system behaves as a porous medium and when it does, what is the appropriate permeability tensor for the medium. A volume of fractured rock can be said to behave like a representative volume of an equivalent porous medium when (1) there is an insignificant change in the value of the equivalent permeability with a small addition or subtraction to the test volume and (2) an equivalent permeability tensor exists which predicts the correct flux when the direction of a constant gradient is changed. A two-dimensional fracture system model is developed. The density, size, orientation, and location of fractures in an impermeable matrix are random variables in the model. Simulated flow tests through the models measure directional permeability, K(,g). A polar coordinate plot of 1/SQRT.(K(,g)) will be an ellipse if the medium behaves like a equivalent anisotropic, homogeneous porous medium. Whatever shape the plot is, a best fit ellipse can be calculated and the scatter of measurments around the ellipse is expressed as NMSE, the normalized mean square error. NMSE approaches zero as the behavior approaches that of a continuum. Studies were performed where fracture length and areal density were varied such that fracture frequency, as would be measured in a borehole was held constant. The examples studied showed the permeability increased with fracture length. In another study the modeling techniques were applied to data from the Atomic Energy of Canada Ltd.'s Underground Research Laboratory facility in Manitoba, Canada. The fracture pattern as exposed at the surface was assumed to persist at depth. Well test data were used to estimate the aperture distribution for the model. Apertures were assigned to the fracture pattern, both by assuming that aperture was and was not positively correlated with fracture length. The permeabilities of models with uncorrelated length and aperture were smaller than for correlated models. The NMSE of certain correlated models may become high due to the production of very long high aperture "super conductors." A Monte Carlo type study showed that analysis of steady state packer tests would consistently underestimate the mean aperture. Finally, extension of the model to three dimensions is discussed where fractures are discs randomly located in space. Intersections between the fractures are line segments. Solution of the steady state flow equations is based on image theory.